ASVAB Mechanical Comprehension Practice Test 733076 Results

	Your Results	Global Average
Questions	5	5
Correct	0	3.13
Score	0%	63%

Review

1 What is the mechanical advantage of this inclined plane if the length of the ramp is 24 ft. and the height of the green box is 8 ft.?

82% Answer Correctly

	3
	2.7
	4.5
	5

Solution

The mechanical advantage (MA) of an inclined plane is the effort distance divided by the resistance distance. In this case, the effort distance is the length of the ramp and the resistance distance is the height of the green box:

MA = \( \frac{d_e}{d_r} \) = \( \frac{24 ft.}{8 ft.} \) = 3

2 If the force applied at the blue arrow over 9 ft. moves the green box 1.0 ft., what is the mechanical advantage of this lever?

56% Answer Correctly

	9
	27
	0
	8.1

Solution

Mechanical advantage (MA) can be calculated knowing only the distance the effort (blue arrow) moves and the distance the resistance (green box) moves. The equation is:

MA = \( \frac{E_d}{R_d} \)

where E_d is the effort distance and R_d is the resistance distance. For this problem, the equation becomes:

MA = \( \frac{9 ft.}{1.0 ft.} \) = 9

You might be wondering how having an effort distance of 9 times the resistance distance is an advantage. Remember the principle of moments. For a lever in equilibrium the effort torque equals the resistance torque. Because torque is force x distance, if the effort distance is 9 times the resistance distance, the effort force must be \( \frac{1}{9} \) the resistance force. You're trading moving 9 times the distance for only having to use \( \frac{1}{9} \) the force.

The mechanical advantage of a wheel and axle is equal to the:

61% Answer Correctly

	length of the axle
	difference in the diameters of the wheels
	ratio of the diameters of the wheels
	difference in the lengths of the axles

Solution

A wheel and axle uses two different diameter wheels mounted to a connecting axle. Force is applied to the larger wheel and large movements of this wheel result in small movements in the smaller wheel. Because a larger movement distance is being translated to a smaller distance, force is increased with a mechanical advantage equal to the ratio of the diameters of the wheels. An example of a wheel and axle is the steering wheel of a car.

4 If the green box weighs 15 lbs. and is 7 ft. from the fulcrum, how far from the fulcrum would a 50 lbs. weight need to be placed to balance the lever?

61% Answer Correctly

	8.4 ft.
	0.7 ft.
	6.3 ft.
	2.1 ft.

Solution

To balance this lever the torques on each side of the fulcrum must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:

R_ad_a = R_bd_b

where a represents the left side of the fulcrum and b the right, R is resistance (weight) and d is the distance from the fulcrum.

Solving for d_b, our missing value, and plugging in our variables yields:

d_b = \( \frac{R_ad_a}{R_b} \) = \( \frac{15 lbs. \times 7 ft.}{50 lbs.} \) = \( \frac{105 ft⋅lb}{50 lbs.} \) = 2.1 ft.

5 The radius of the axle is 5, the radius of the wheel is 10, and the blue box weighs 75 lbs. What is the effort force necessary to balance the load?

53% Answer Correctly

	15 lbs.
	37.5 lbs.
	10 lbs.
	7 lbs.

Solution

The mechanical advantage of a wheel and axle is the input radius divided by the output radius:

MA = \( \frac{r_i}{r_o} \)

In this case, the input radius (where the effort force is being applied) is 10 and the output radius (where the resistance is being applied) is 5 for a mechanical advantage of \( \frac{10}{5} \) = 2.0

MA = \( \frac{load}{effort} \) so effort = \( \frac{load}{MA} \) = \( \frac{75 lbs.}{2.0} \) = 37.5 lbs.